| 非满等距映射的线性延拓 |
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| 引用本文： | 王瑞东.非满等距映射的线性延拓[J].数学学报,2006,49(6):1335-133. |
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| 作者姓名： | 王瑞东 |
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| 作者单位： | 南开大学数学科学学院,天津300071 |
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| 基金项目： | 国家自然科学基金资助项目（10571090）;高校博士点基金资助项目（20010055013）.衷心感谢定光桂教授的悉心指导和帮助,还感谢审稿人对本文提出十分宝贵的建议. |
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| 摘 要： | 主要研究实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题．得到：若等距映射V_0：S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V：E→F,这是我们首次在非满的情况下考虑Tingley问题．
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| 关 键 词： | Tingley问题 等距 线性延拓 |
| 文章编号： | 0583-1431（2006）06-1335-04 |
| 收稿时间： | 2005-04-30 |
| 修稿时间： | 2005-04-302005-09-15 |
On Linear Extension of Isometries Between Unit Spheres |
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| Rui Dong WANG.On Linear Extension of Isometries Between Unit Spheres[J].Acta Mathematica Sinica,2006,49(6):1335-133. |
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| Authors: | Rui Dong WANG |
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| Institution: | School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China |
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| Abstract: | we study the extension of isometries between the unit spheres S_1 (E) and S_1 (F),where E and F are both real normed spaces.We obtain that if the non-surjective isometry V_0 from S_1 (E) to S_1 (F) satisfy some properties,the V_0 can be extended to be real linearly isometric map V of E into F.This is the first time we study Tingley' problem without the condition of surjectivity. |
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| Keywords: | Tingley problem isometry extension of isometry |
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